Answer:
0x^2 + 2x -3 = 0
a = 0
b = 2
c = -3
Step-by-step explanation:
3 = 2x
0 = 2x - 3 (move three to other side)
0x^2 + 2x -3 = 0 (Finish off the equation by adding zeros in the empty spots to make the eeqution ax^2 + bx + c = 0)
a = 0
b = 2
c = -3
Marianne opened a retirement account that has an annual yield of 5.5%. She is planning to retire in 25 years. How much should she put into the account each month so that she will have $500,000 when she retires?
Answer:
Monthly deposit, P = $776.41
Step-by-step explanation:
Interest rate per annum = 5.5%
number of years = 25
Since she pays monthly, number of payments per annum = 12
Interest rate per period, r = (Interest rate per annum)/(number of payments per annum)
r = 5.5%/12 = 0.46%
Number of periods, n = number of years * number of payments per annum
n = 25 * 12 = 300
Future value of annuity, FVA = $500,000
Monthly deposit will be:
[tex]P = \frac{(FVA) * r}{(1+r)^{n} -1} \\P = \frac{(500000) * 0.46/100}{(1+0.46/100)^{300}-1 }[/tex]
P = $776.41
Answer:
MP = $778.77
she should put $778.77 into the account each month
Step-by-step explanation:
This problem can be solved using the compound interest formula;
FV = MP{[(1+r/n)^(nt) - 1]/(r/n)} .......1
Where;
FV = Future value
MP = monthly contribution
r = yearly rate
n = number of times interest is compounded per year.
t = number of years
Given
FV = $500,000
t = 25 years
r = 5.5% = 0.055
n = 12 months/year
From equation 1, making MP the subject of formula;
MP = FV/{[(1+r/n)^(nt) - 1]/(r/n)}
Substituting the given values we have;
MP = 500,000/(((1+0.055/12)^(12×25) -1)/(0.055/12))
MP = $778.77
she should put $778.77 into the account each month
Ana ha comprado libros, todos del mismo precio, por valor de 120 euros. El librero le regala 3 libros por lo que cada libro le cuesta 2 euros menos. ¿Cuántos libros ha comprado?
Answer:
El primer paso será darle un nombre a nuestras variables:
x= Numero de libros comprados inicialmente
y=Precio inicial de los libros
Ahora analizamos el enunciado,
Lorena ha comprado libros todos del mismo precio por valor de 120 €
x*y=120 € (1)
El librero le regala 3 libros por lo que en realidad cada libro que cuesta 2 € menos
(x+3)(y-2)=120€ (2)
Tenemos entonces dos ecuaciones con dos incógnitas, así que podemos resolver,
Despejamos en (1)
x=120/y
Sustituimos en (2)
(120/y +3)(y-2)=120
120 - 240/y + 3y -6 =120
3y-240/y =120-120+6
3y -240/y =6
y- 80/y=6
y²-80=6y
y²-6y-80=0
Resolvemos la ecuación de segundo grado
a=1
b=-6
c=-80
Aplicando la resolvente,
(6+- √36+320)/2
6+-√356/2
(6+-18,86)/2
Como el valor de y no puede ser negativo la unica respuesta válida será:
y=12,43
Cada libro le costo 12,43€
Sustituyendo en (1)
x=120/12,43
x=9,65 como no puede ser un número racional
x=9
Lorena ha comprado 9 libros
Ana originally bought 12 books.
Explanation:Let's say Ana originally bought x books, each costing p euros.
The total cost of all the books is 120 euros, so we can write the equation:
x * p = 120
After the bookseller gives Ana 3 free books, the new total number of books she has is x + 3 and each book costs p - 2 euros.
The new total cost of all the books is still 120 euros, so we can write the equation:
(x + 3) * (p - 2) = 120
Simplifying this equation, we get:
px + 3p - 2x - 6 = 120
Combining like terms:
px - 2x + 3p - 6 = 120
Substituting the equation px = 120, we get:
120 - 2x + 3p - 6 = 120
Simplifying further:
3p - 2x - 6 = 0
Let's rewrite this equation:
3p - 2x = 6
When we substitute the equation px = 120 into this equation:
3p - 2(120/p) = 6
Simplifying:
3p - 240/p = 6
Multiplying through by p:
3p^2 - 240 = 6p
Rearranging:
3p^2 - 6p - 240 = 0
Using the quadratic formula to solve for p:
p = (-(-6) ± sqrt((-6)^2 - 4*3*(-240)))/2*3
p = (6 ± sqrt(36 + 2880))/6
p = (6 ± sqrt(2916))/6
p = (6 ± 54)/6
For the positive value of p:
p = (6 + 54)/6 = 60/6 = 10
Now, substituting p = 10 back into the equation px = 120:
10x = 120
x = 120/10 = 12
So, Ana originally bought 12 books.
A maps key shows that every of 5 inch on the map represents 200 miles of actual distance the distance between two cities on the map is 7 inches right to be used to find the actual distance
Answer:
280 miles of actual
Step-by-step explanation:
Given that:
The distance between two cities on the map : 7 inches5 inch on the map represents 200 miles of actual<=> 1 inch on the map represents : 200/5 = 40 miles of actual
So the actual distance between the 2 cities is:
7*40 miles of actual
= 280 miles of actual
Hope it will find you well.
Jessica gets her favorite shade of purple by mixing 1/3 cup of blue with 1/2 of red. How many of blue and red paint does Jessica need to make 20 cups of her favorite purple paint?
Answer:
8 cup of blue
12 cup of red
Step-by-step explanation:
The first thing is to calculate how much black paint is produced, assuming that the volumes add up, we have to:
1/2 + 1/3 = 5/6
5/6 cup of paint is produced, I want to know how much I need to produce 20 cups, I divide the value I want by the ideal value, that is, 5/6 and thus I obtain the factor that I require:
20 / (5/6) = 24
Now I multiply by 24 each quantity of blue and red paint
1/2 * 24 = 12
1/3 * 24 = 8
Which means you need 12 cups of red paint and 8 cups of blue paint
Which algebraic expression represents this phrase?
the product of 40 and the distance to the finish line
THE ANSWER WOULD BE 40 × d
or 40d
The students in Brenna's grade voted to select a guest speaker. 15 students voted for a
famous athlete. The other 45 students in Brenna's grade voted for a famous actor. What
percentage of the students voted for the athlete?
Write your answer using a percent sign (%)
Final answer:
To find the percent of students who voted for the athlete, divide the number of students who voted for the athlete by the total number of students, and then multiply by 100. This results in 25% of the students voting for the athlete.
Explanation:
To calculate the percentage of students who voted for the athlete, you would use the formula: part over total, times one hundred, equals percent. In this case, the part is the number of students who voted for the athlete (15), and the total is the combined number of students who voted for the athlete and actor (15 + 45).
So, the calculation would be as follows: (15 / (15 + 45)) x 100 = (15 / 60) x 100 = 0.25 x 100 = 25%. Therefore, 25% of the students voted for the athlete.
Mrs.Long wants to rent a bounce house for her owens birthday. Inflate a rentals charges a 145 fee plus 35 per hour. If Mrs. Long paid 355 total, how many hours did she rent the bounce house for
Answer:
The correct answer is 6 hours.
Step-by-step explanation:
Let Mrs. Long rent the bounce house for x hours.
Fixed price to be charged is 145.
Per hour price of the bounce house is 35. Total price of x hours is 35x.
Thus total amount charged by the rentals is 145 + 35x.
Mrs. Long paid 355 in total.
∴ 145 + 35x = 355
⇒ 35x = 210
⇒ x = 6.
Thus Mrs. Long rented the bounce house for 6 hours.
I need help, how many chirps per minute?? and why?
Which measurement statement is correct?
There are 2 cups in a pint.
There are 2 pints in a cup.
There are 4 quarts in a pint.
There are 4 pints in a quart.
Answer:
There are 2 cups in a pint is correct
The correct measurement statement is that there are 4 pints in a quart. This conclusion is derived from understanding the relationship between cups, pints, and quarts in the customary system of measurement.
Explanation:The correct measurement statement among the options provided is that there are 4 pints in a quart. This is because, in the customary system of measurement, one quart (qt) is equivalent to two pints (pt), and a pint is equivalent to two cups (c). Therefore, the relationship among these units of measure can be summarized as follows:
1 quart = 2 pints1 pint = 2 cupsThus, when we compare cups, pints, and quarts, we establish that the conversion factors are essential for accurate measurement in different scenarios, whether it be for cooking or scientific measurements.
Plz help asap!!!!!!!!!!!!!!!!!!!
Answer:
A) 0.685
Step-by-step explanation:
P(no snow) = 1 - P(snow)
1 - 0.315
0.685
The Castel del Monte in Apulia, Italy, was built more than 750 years ago. The fortress has one central building with eight surrounding towers. Which polygon do you see repeated in the structure? How many sides, angles, and verticles does this polygon have?
Answer:
Polygon: Octagon
Sides: 8
Angles: 8
Vertices: 8
Total interior angle: 1080
Step-by-step explanation:
8 sides so it's an octagonal figure,
8 sides, 8 vertices and 8 angles
Total angle:
(8 - 2)×180
1080
From least to greatest, what are the measures of the next two angles with positive measure that are coterminal with an angle measuring 250°?
Answer:
610 and 970
Step-by-step explanation:
Answer:
610 and 970
Step-by-step explanation:
The population of Leavetown is 123,000 and is decreasing at a rate of 2.375% each year.
What will the population of Leavetown be 100 years from now?
The population of Leavetown after 100 years would be 111,17.5681.
Step-by-step explanation:
Given that,
Initial Population = I = 123,000
Decreasing Rate = r = 2.375 = 0.02375
We have to find the population after 100 years. So,
n = 100
The formula to calculate the population (P) after n years with a decreasing rate r is:
[tex]P = I (1-r)^{n}[/tex]
Now, put the values in this formula.
[tex]P = 123,000 (1-0.02375)^{100}[/tex]
[tex]P = 123,000 (0.97625)^{100}[/tex]
[tex]P = 11117.5681[/tex]
Hence, the population of Leavetown after 100 years would be 111,17.5681.
4.
Find the domain of the following function:
y = x3 − 8
_________
x2 + 9
Select the appropriate response:
A) 483xy
B) domain: all values of y
C) all values of x
D) Not possible to solve
Answer:
C) all values of x
Step-by-step explanation:
The denominator has no real roots which means it's not 0 for any x. Hence x can take any real value
Answer:
C
Step-by-step explanation:
All values of x
I hope this is what you need
in 56 years,Kevin will be 9 times as old as he is right now .
How old is he right now ?
Answer:
Kevin is 7
Step-by-step explanation:
In 56 years if Kevin is 7 now he will be 63 and 7X9 = 63
Create a rational expression that satisfies the following criteria: 1) Domain is all reals except 1 and -1 2) x=1 is a vertical asymptote 3) X = -1 is a hole 4) There is a horizontal asymptote at y = 3
Answer:
y = (3x² + x - 2)/(x² - 1)
Step-by-step explanation:
(x - 1)(x + 1) = x² - 1
In the denominator
f(x)/(x² - 1)
f(x) has a factor (x + 1)
3 + (x + 1)/(x² - 1)
(3x² - 3 + x + 1)/(x² - 1)
y = (3x² + x - 2)/(x² - 1)
The American Academy of Family Physicians released a survey, revealing that 76% of US adults admit they lie to their doctor about how often they exercise. Dr. Moffett believes the percentage seems high, so she decides to conduct her own hypothesis test to determine the true proportion. What should she write as the null and alternative hypotheses for this situation?
Answer:
H₀: p=0.76
Ha :p < 0.76
Step-by-step explanation:
A null hypothesis is the common accepted fact that the researcher works to prove it wrong. In this case, the survey revealed that 76% of US adults admit they lie to their doctor about how often they exercise. This forms the null hypothesis.
The alternative hypothesis suggest that a new theory is happening unlike the original one.In this case, Dr. Moffett believes the percentage seems high, so the alternative hypothesis is that the percentage is lower than 76%
Answer:
H0: p = 0.76; Ha: p < 0.76
Step-by-step explanation:
I took the quiz and got it right
The miles-per-gallon obtained by the 1995 model Z cars is normally distributed with a mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon. What is the probability that a car will get less than 21 miles-per-gallon?
Answer:
0.42074
Step-by-step explanation:
In this question, we are asked to calculate the probability that a car will get less than 21 miles per gallon.
This is P(x < 21)
z = 21-22/5 = -1/5 = -0.2
Therefore the probability of getting less than 21 miles per gallon will be;
P(x<21) = P (z < -0.2)
= 0.42074
Three identical bags each contain two marbles. One bag has two white marbles, one has two black marbles, and one has one of each. You are given a bag at random and draw a white marble. What fraction of the time will the second marble you draw from that bag also be white?
Answer:
2/3
Step-by-step explanation:
All possible outcomes for flipping a coin three times are listed below (hhh,hth,hht,tth,tht,htt,ttt what is the probability of obtains at least 2 heads
Final answer:
To find the probability of getting at least 2 heads in three coin tosses, count the favorable outcomes (HHH, HHT, HTH, THH) and divide by the total outcomes. The probability is 4/8 or 1/2, which is 50%.
Explanation:
The question asks to calculate the probability of getting at least 2 heads when flipping a coin three times. The sample space for three coin tosses consists of 8 possible outcomes: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. To find the probability of getting at least 2 heads, we need to count the favorable outcomes which are: {HHH, HHT, HTH, THH}, and then divide this number by the total number of possible outcomes.
There are 4 favorable outcomes out of 8 possible, so the probability is 4/8 or 1/2. Therefore, the probability of obtaining at least 2 heads in three coin tosses is 0.5 or 50%.
What is the first quartile of the box-and-whisker plot
Answer:
Between 36 and 38
Answer:
girl, is that USA Test Prep???
im doing that also!!
i think its between 36 and 38 basically.
Step-by-step explanation:
hope it helps i guess!! <33
Here are the first five terms of Fibonacci sequence.
4, 4, 8, 12, 20
a) Write down the next two terms in the sequence ... , ...
The first three terms of a Fibonacci sequence are
n, 3n, 4n
b) Find the sixth term of this sequence
Answer:
a) 32, 52
b) 18n
Step-by-step explanation:
a)
12+20=32
20+32=52
b)
4th element = 3n+4n=7n
5th element = 4n+7n=11n
6th element = 7n+11n=18n
Answer:
a) 32, 52
b) 18n
Step-by-step explanation:
because 7n+n
3n+7
4
Which dimensions can create more than one triangle? A. Three angles measuring 75 degrees, 45 degrees, and 60 degrees. B. Three sides measuring 7m, 10m, 12m. C. Three angles measuring 40 degrees, 50 degrees, 60 degrees. D. Three sides measuring 3 cm, 4cm,5cm
The answer is C
Because the sum of the angles are not up to 180
which makes way for other angles.
Option B, three side lengths measuring 7m, 10m, and 12m can create more than one triangle because there are multiple ways the sides can be oriented to create different internal angles, therefore creating multiple triangles.
The question is about constructing triangles from given dimensions and determining which sets of dimensions can create more than one triangle. In geometry, for a set of dimensions to produce more than one unique triangle, it must not fully determine the shape of the triangle. The axiom that the sum of the angles in a triangle is exactly 180 degrees is key to answering part of this question. Here are the evaluations based on the given options:
A set of angles that sum to 180 degrees will only create one unique triangle.For three given side lengths, as in option B, if they satisfy the triangle inequality theorem (the sum of the lengths of any two sides must be greater than the length of the remaining side), they will create a unique triangle.A set of angles less than 180 degrees does not create a valid triangle.For three given side lengths that form a right triangle (such as a 3-4-5 triangle), if they also satisfy the Pythagorean theorem, they will create a unique triangle.Upon evaluating the provided dimensions:
Option A: Angles of 75 degrees, 45 degrees, and 60 degrees sum to exactly 180 degrees, forming one unique triangle.Option B: Sides measuring 7m, 10m, 12m can create more than one triangle due to the possibility of different internal angles based on different orientations of the sides.Option C: Angles of 40 degrees, 50 degrees, and 60 degrees only sum to 150 degrees, so no valid triangle can be created.Option D: Sides measuring 3 cm, 4 cm, 5 cm form a unique right triangle, not more than one.Therefore, the correct answer is B: Three sides measuring 7m, 10m, 12m can create more than one triangle.
A line segment has end points at (4, -6) and (0, 2) what is the slope of the given like segment
Answer:
The slope is -2
Step-by-step explanation:
-6-2/4-0=-8/4=-2
Answer:
The slope is -2
Step-by-step explanation:
We can find the slope of a line given two points using
m = (y2-y1)/(x2-x1)
= (2 - -6)/(0 -4)
= (2+6)/(0-4)
= 8/-4
= -2
A bridge over a river has the shape of a circular arc. The span of the bridge is 24 meters. (The span is the length of the chord of the arc.) The midpoint of the arc is 4 meters higher than the endpoints. What is the radius of the circle that contains this arc
Answer:
20 meters
Step-by-step explanation:
Seeing the image attached, we can observe that there is a triangle formed by half of the chord of the arc, the radius (hypotenusa) and part of the radius (r-4). Using pythagoras theorem in this triangle, we have:
(r-4)^2 + 12^2 = r^2
r^2 - 8r + 16 + 144 = r^2
8r = 160
r = 20
So the radius of the circle that contains this arc is 20 meters.
Answer:
20 m
Step-by-step explanation:
radius 'r', half the chord, and dist from center to the chord has formed a right angle triangle
where,
r is hypotenuse
(r-4) = one side i.e dist from center to chord)
12 = other side i.e half the length of the chord)
By applying Pythagoras theorem, we will have
r² = 12² + (r-4)²
r²= 144 + r² - 8r + 16 --->(cancel out r²)
0 = -8r + 160
8r = 160
r = 160/8
r = 20 m
Thus, the radius of the circle containing this arc is 20m
You can also verify this :
distance from center to chord: 20 - 4 = 16
r = [tex]\sqrt{16^{2}+12^{2} }[/tex]
r = 20
A filing cabinet has a height of 6 feet and a length of 2 feet. The volume of the filing cabinet is 36 cubic feet. What is the width of the filing cabinet?
Answer:
3 feet
Step-by-step explanation:
GIVEN: A filing cabinet has a height of [tex]6\text{ feet}[/tex] and a length of [tex]2\text{ feet}[/tex]. The volume of the filing cabinet is [tex]36\text{ feet}^3[/tex].
TO FIND: What is the width of the filing cabinet.
SOLUTION:
Let the width of filing cabinet be [tex]x\text{ feet}[/tex]
length of filing cabinet [tex]=6\text{ feet}[/tex]
height of filing cabinet [tex]=2\text{ feet}[/tex]
Volume of filing cabinet [tex]=\text{length}\times\text{height}\times\text{width}=36\text{ feet}^3[/tex]
putting values,
[tex]6\times2\times x=36[/tex]
[tex]12\times x=36[/tex]
[tex]x=3[/tex]
Hence the width of filing cabinet is 3 feet.
what is coterminal angle
Answer: Angles who share the same initial side and terminal sides.
whats 7/12 of a full rotation?
Pls mark Brainliest.
Answer:
210°
Step-by-step explanation:
360° is a full rotation. 'Of' also represents a multiplication sign in some places. It basically means that 7/12 of a full rotation is the same as 7/12 * 360° which is equal to 210°.
The equivalent of 7/12 of a full rotation (360°) is; 210°.
According to the question;
The equivalent of 7/12 of a full rotation is to be the determined.We must however remember that a full rotation is given as the angle at a point;
In essence, a full rotation in degrees is 360°.
Consequently;
7/12 of a full rotation = (7/12) × 360°= 7 × 30= 210°Read more:
https://brainly.com/question/2422380
Consider a school with two classes, A and B. In class A there are 15 girls and 17 boys. In class B, there are 19 girls and 10 boys. Both classes plan extracurricular activities for which each class forms a committee consisting of three students. How many possible committees are there such that the total of committee members of both classes combined consists of 4 girls
Answer: 7700 committee
Step-by-step explanation:
Given that In class A there are 15 girls and 17 boys. And In class B, there are 19 girls and 10 boys
To find possible committees of 3 such that the total of committee members of both classes combined consists of 4 girls, we will use combination technique
(15C2 × 17C1) + (19C2 × 10C1)
Or
(15C1× 17C2) + (19C3 ×10C0)
Or
(15C3 × 17C0) + (19C1 × 10C2)
Note that "or" means addition
(1785 + 1710) + (2040 + 855) + (455 + 855)
= 3495 + 2895 + 1310
= 7700 committee
Andrea was chosen to participate in a game show. At the end of the
first round, she had a score of -250. At the end of the second round,
she had a score of 600. How many points did Andrea score during the
second round?
its 350 because you -250 + 650 = 350